In normal operation, the Modified Discrete Cosine Transform (MDCT) has features which make it a well suited tool for audio coding applications. It generates a critically sampled spectral signal representation from overlapping frames and provides perfect reconstruction. This means that the input signal can be reconstructed from spectral coefficients of a forward transform by applying the backward transform and an overlap-add operation in the overlap regions. However, if additional processing is applied on the spectral coefficients, the MDCT has some drawbacks in comparison to oversampled representations like DFT based overlapped processing. Even relatively simple time and frequency dependent gain control, such as used for dynamic range control or clipping prevention can produce unwanted side effects. Therefore, DFT based separate post-processing to audio decoding is applied in several applications which involve this kind of signal modification, although an MDCT based spectral representation would be available inside the decoder. One drawback besides computational complexity is the additional delay introduced by such a post-processing.
A common approach for MDCT time domain aliasing reduction is to recreate an oversampled modulated complex lapped transform (MCLT). The MCLT results from combining the MDCT with its complex counterpart, the Modified Discrete Sine Transform (MDST). The MCLT offers similar features like a DFT representation of a signal and therefore its robustness against time domain aliasing (TDA) due to spectral manipulation is comparable to the DFT representation. But unfortunately calculating the MDST spectrum out of the MDCT spectrum is computationally very complex and produces a significant signal delay. Hence, the state-of-the-art provides techniques for reducing both delay and complexity [See Kuech, F.; Edler, B., “Aliasing Reduction for Modified Discrete Cosine Transform Domain Filtering and its Application to Speech Enhancement”, in IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 21-24 Oct. 2007; and Edler, B., “Aliasing Reduction for Gain Control with Critically Sampled Filter Banks”, in First International Conference on Communications and Electronics, ICCE '06, 10-11 Oct. 2006]. In these approaches, a real-to-complex (R2C) transform is used to approximate the MDST values that may be used. Then in the MCLT domain the manipulation of the spectral coefficients is applied. Afterwards, the complex values are transformed into the MDCT domain again using a complex-to-real (C2R) transform. Although this approach delivers good results in terms of aliasing robustness, it has some disadvantages. First, the MDST coefficients are estimated and their accuracy is defined by the amount of computational complexity. Second, the transform chain R2C-C2R produces still delay.